The `Blow` hitmaker admires the young pop superstar and thinks a duet between them would be great.
Ke$ha has a very eclectic music taste and can imagine herself just as easily recording with legendary Rolling Stones guitarist Keith Richards.
She said: "The range of artists I want to workwith is so vast, it`s bizarre. I would love to have Keith Richards on the record. I would sure as hell like to do a collaboration withBieber and at the same time do a song with the Flaming Lips. If someone is a real artist, you can`t confine them to a particular genre. It`s my mission to make it all make sense somehow."
The 25-year-old singer is very proud of the success she has achieved so far in her career but although she has topped charts all over the globe she still feels like the "dirty little sister" of the biggest pop stars.
In an interview with V magazine, she contemplated: "I do feel like there are the pop stars of the world and then I`m like their dirty little sister, running around with s**t on my face in combat boots because I can`t walk in heels."
Ke$ha believes her outsider mentality comes from the fact her mother Pebe raised her and her older brother Lagan as a single parent and things were tough for the three of them.
The pop beauty - who has no knowledge of her father`s identity - also had a hard time at high school and she wants her difficult experiences to inspire her fans.
She explained: "I try to include my fans in my message. I do feel like there is an element of what I`m doing that is about where I come from, which is working-class. I was never the cool kid, I was never hot in high school. I was never popular. You don`t have to be perfect and you don`t have to be rich and you can still be successful."